Poole Ch.P., Jr. Handbook of Superconductivity
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4~
Table 9.5.
Lower (Bcl, mT), and upper (Bc2 , T) critical magnetic fields perpendicular to (Bab, Bc2) ,ab and parallel
to (BcCl ,
BC2) the c axis for various superconductors. Values for the
critical temperature T c and the upper critical field derivatives at T c namely -B~ b'
ab _BUcc2 dBC2
, = dBc2/dT and =
/dT
for the perpendicular and parallel cases, respectively,
are also given. References are identified by first author and year.
Material Tc Bab BcCl B~c b /~c2 -B~c b' -BC'2 Comments Reference
(K) (mT) (mT) (T) (T) (T/K) (T/K)
Nb 9.3 0.57 0.31
UPd2A12
Nb3S 4 3.65
CeCu2Si 2 0.63
UPd2A13 1.91
YNi2B2C 15
fl-(ET)2I 3 1.5
fl-(ET)213
fl-(ET)EIBr2
2.3
fl-(ET)2AuI 2 4.2
K-(ET)2 Cu[N(CN)2 ]Br 11.6
(TMTSF)2C104 1.06
(Sm0.925 Ceo.ov5)2CuO 4
11.4
(ta0.925Cao.075)2CuO 4 ~ 14
(La0.925 Ca0.075)2 CuO4 30
(La0.925 Cao.075)2CuO 4 ~,~ 34
YBa2Cu306. 5 62
YBa2Cu306.9
YBa2Cu3 O6.94 91.2
YBa2Cu3 O7_,5 87
7 36
390
400
0.055
7
2.5
23
1600
2050
0.24
30
8.3
95
32
BC2 is value meas. I film Oya (1989)
B ab
is value meas. II film
5.8 4.9 Thin film, temperature, and Hessert (1997)
angular dependence
0.5 2.1 zig-zag Nb-Nb-Nb- chains Biberacher (1980)
2.0 2.4 Heavy electron Assmus (1984)
3.5 4.1 6.5 5.6 Heavy electron Hessert (1995)
7 8.3 Meas at 4.2 K Arisawa (1995)
1.74 0.08
ab
values are averages of Ishiguro (1990)
measurements along a and b
25 2.7 Organic, at 1.6 kbar Ishiguro (1990)
3.48 1.5
ab
values are averages of Ishiguro (1990)
measurements along a and b
6.35 ~ 0.8 Organic material Ishiguro (1990)
20 2.2 Organic material Kwok (1990)
Bbl -- 0.055 Schwenk (1984)
28.2 5.2 3.6 0.1 Electron type material Dalichaouch (1990)
> 20 > 13 4 0.3 Hidaka (1987)
32 1.5 Li (1993)
Naito (1990)
380 87 8.7 2.0 Vandervoort (1991)
Monocrystal Moschalkov (1991 )
115 1.8 Ossandon (1992)
145 72 Films on (100) SrTiO3 Topchishvili (1991)
DyBa2Cu307
EuBa2Cu307
Yo.8 Pro.2Ba2Cu3 O6.9
Bi2.1Sr2.1Cao.9Cu2.008+6
Bi2 Sr2CaCu208+6
(B i,Pb)2 S rz CaCu2 O8
Bi2 SrzCazCu308
Bil.7 Pb0.7 Sr2 Ca2
CU 3 010
Pb 2 Sr 2 (Y, Ca)Cuz 08
T1BaCaCuO
HgBa2Ca2Cu308+6
92.4
90
92
95
94.8
73
85
80
90
86
91
109
110
76
131
~<5
24
18
11.3
85
6.3
9.5
500
95
53
34
50.5
45
100
240
110
100
190
245
174
542
50
39
590
34
40
45
28
56
71.5
89
1000
198
96
190
3.8
3.4
10.5
3.0
3.8
3.4
8.5
16
11
20
0.54
1.0
1.9
0.7
0.41
1.1
0.56
1.4
0.5
1.75
0.6
2.0
Thin film measured
at 4.2K
B c = 1.93
See 42 table
Measured at 4.2 K
Monocrystal
Oriented thin film
Microwave absorption
B c = 0.65
Birre v -- 24 T
Ag-clad tape
Monocrystal
Thin film, pulsed fields;
see 42 table
Basovich (1992)
Gallagher (1988); see also
Worthington (1987)
Salamon (1989), Malozemoff
(1989)
Nakao (1993)
Krushin-Elbaum (1989)
Scheidt (1989)
Welp (1989a,b)
Hampshire (1988)
Hikita (1987)
Tajima (1988)
Jia (1992)
Li (1988)
Kang (1988)
Maeda (1992)
Misra (1992)
Zhang (1992)
Matsubara (1992)
Matushita (1993)
Babic (1995)
Reedyk (1992)
Staguhn (1989)
Schilling (1994)
4~
-,,4
458 Chapter 9: Characteristic Parameters
The upper critical field slope (22b) is of especial interest for materials such as the
cuprates in which it is often not feasible to reach high enough applied fields to
experimentally determine Bc2 directly.
The thermodynamic critical field B c is not usually measured directly, but
can be calculated from the expressions
,v/2tcBcl
Bc2
(BclBc2) 1/2
Be - In x = ~/2----~ = (In K) 1/2 (24)
if the Ginzburg-Landau parameter ~ is known. We also have the quotient relation
Bc2/Bcl
- 2tc 2 / In to, (25)
and of course we know that x = 2/~. The lower, thermodynamic, and upper
critical fields in the isotropic high tc approximation (to >> 1 so Bcl << B c << Bc2 )
are related to the coherence length ~ and penetration depth 2 through Eqs. (7), (8),
and (4), respectively. Equations (4) and (7) can be used to estimate ~ and 2,
respectively, when Bc2 and Bca are known.
Many superconductors are anisotropic, and Table 9.5 lists critical fields for
axially symmetric materials. Also listed are the upper critical field slopes (22b)
for the perpendicular
r_Rab'
~, ~c2 )
and parallel (-Bc'2) cases. We see from the data that
the slope
_Rab'
for the cuprates tends to exceed the Pauli limit value 1.83 T/K of
a-,c2
r
Eq. (23), and -Bc2 tends to be less than this value. This occurs because ordinarily
>
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Table
9.6.
Critical current density Je for various superconductors. Values for the temperature Tmeas and the field Bap p of measurement are also given. References are identified by
first author and year.
Material Jc
Bap p
Tmeas Comments Reference
(A/cm 2) (tesla) (K)
4~
Melt textured high-T c
materiels
Cu-Nb composite
NbTi
NbN
0.02 to 1 77 Jc ~ [1 -
(T/Tc)]~/B #,
where ~ ~< 7, Fisher (1994)
#~0.5
2.5 x 105 Self field 4.2 T c = 8.8 K Reddy (1986)
3.4 x 105 5 4.2 Superconducting composite Li (1983)
3 • 105 5 Filament diameters 5 to 9 pm Kanithi (1989)
3 x 105 0.5 4.2 Filament diameter 50-500nm; see ~2 Cave (1989)
table
1.41 x 106 1 Wire enclosed by CuNi alloy, Kumano (1990)
0.072 pm filament diameter, Jc is less
for 0.061/~m filament diameter
1.07 x 106 1 0.4 #m filament, artificial pinning Miura (1992)
control
4.44 x 105 3 0.4/~m filament, artificial pinning Miura (1992)
control
5.2 x 105 5 4.2 47 wt% Ti, filaments are aligned Cooley (1991)
2.85 x 105 5 48 wt%Ti, 210 filament, 1.6 mm Chernyi (1997)
diameter wire
3.5 x 105 5 4.2 Industrial wires Chemoplekov (1992)
3.36 x 105 3 Wire, 54 wt% Ti Inoue (1995)
4.6 x 105 5 4.2 Artificial pinning center wire, Heussner (1997)
47 wt%Ti
2 x 104 0 Josephson junction 1.5 #m 2 area Tarutani (1984)
(continued)
4~
Material
Nb carbonitride
NbN/A1N/NbN
Nb, Nbo.sZro. 5 multilayer
V2(Hf, Zr ) Laves
MxM06 S8Chevrel
PbM06S 8 Chevrel
Table 9.6. (continued)
J~
(A/cm 2)
Bapp
(tesla)
meas
(K)
Comments
6.5 x 10
4
1 x 10 4
> 10 7
8x 10 5
1-5 x 10 5
10 6
10 4
106
3 x 104
103
5.4 x 104
1.2 x 105
1 x
104
2x 104
2x 104
1.8 x 10 4
1.6 x 10 4
9.5 x 103
4.8 x 10 3
4 x 10 4
10 4
1.8 x 10 3
15
20
0
13
0
13
0
14
18
0
17
20
8
14
20
23
26
10
17
27
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
20
4.2
1.8
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
Tape, parallel field, see B c table;
re= 15.6K
Tape, parallel field, see B c table;
~r 15.6K
Extrapolated value, thin film; see B e
table
Film; see B c table
Layers 50-80 nm thick; see B c table
T c -- 15- 17 K; see B e table,
NbCl_yNy
T c = 15 - 17 K; see B e table,
NbCl_yNy
Film
Film
Film
Tunnel junction
Anisotropy effects
Multifilamentary wire
Multifilamentary wire
Tape
Hot isostatic-pressed wire
Hot isostatic-pressed wire
Hot isostatic-pressed wire
Calculated by Kramers' scaling law
Monofilamentary wire
Monofilamentary wire
Reference
Suzuki (1989)
Suzuki (1989)
Boffa (1996)
Gavaler (1983)
Dietrich (1987)
Dietrich (1983)
Dietrich (1983)
Brunet (1979)
Brunet (1979)
Brunet (1979)
Zhen (1997)
Kuwasawa (1990, 1991)
Inoue (1985)
Inoue (1985)
Alekseevskii (1977)
Hamasaki (1985)
Yamasaki (1992, 1988)
Yamasaki (1992, 1988)
Yamasaki (1992, 1988)
Ramsbottom (1997)
Hamasaki (1989)
Hamasaki (1989)
q~
SnM06S 8 and
Pbo.6Sno.4M06S8
Pbo.6 Sno.4M06 S 8 Chevrel
Pbl.2Mo6S7. 8 Chevrel
Pb1.2 Mo6.4 $8 Chevrel
Pb-Mo-S Chevrel
Pb-Mo-S Chevrel
Chevrel
V3Ga, A 15
Nb3A1, A15
Nb3Ge, A15
Nb3Sn , A15
Range 10 5 to 5 x 10 3
> 105
5 x 104
1.3 • 104
3.5 x 104
> 106
5 x 104
5.4 x 104
3.1 x 104
2x 106
1.6 x 106
1 xlO 5
> 104
4.86 x 104
1.95 • 104
1.13 • 105
104
104
104
103
2x 104
2 x 101~
105
3 x 104
6.7 x 104
3.7 x 104
4 x 104
10
15
23
14
0
8
20
24
10
9
20
23
20
20
12
18.8
16
17.5
Self field
20
5
15
15
20
20
12
4.2
4.2
4.2
1.7
1.9
1.9
4.2
4.2
4.2
1.8
4.2
4.2
4.2
19
4.2
4.2
1.8
4.2
Monofilament Chevrel wires
Coils of 1 meter wire
Coils of 1 meter wire
Wire
Wire with Nb as antidiffusion barrier
Wire with Nb as antidiffusion barrier
Multifilamentary wire
Single core wire
Tapes with Ge doping for A1
Composite wire; see B c table
Composite wire; see B c table
Wire
Wire, T c = 17 K
Wire, T c = 15.7 K
Wire, powder metallurgy
Sapphire substrate, T c = 22.4 K
Nb3Ge deposited on 0.1 mm thick
tapes
Fast neutron irradiated wires
2 at.% Ti in Nb core
Bap p parallel to tape surface
Bronze processed multifilamentary
wires
Bronze processed multifilamentary
wires
Al-stabilized strand
Gupta (1995)
Cheggour (1995)
Cheggour (1995)
Kubo (1989)
Alekseevskii (1982)
Hamasaki (1982)
Hamasaki (1982)
Cheggour (1997)
Cheggour (1997)
Francavilla (1979)
Sharma (1981)
Sharma (1987)
Kumakura (1990)
Fukuda (1997)
Fukuda (1997)
Ayai (1997)
Saito (1990)
Watanabe (1990)
Watanabe (1987)
Oya (1979)
Nakagawa (1987)
Brown (1978)
Tachikawa (1981)
Yoshida (1983)
Suenaga (1984)
Suenaga (1984)
Takahashi
(1985)
(continued)